A master public key serving as the basis of all ciphertexts and a master secret key serving as the basis of all user secret keys exist for ID-based encryption, attribute-based encryption, and functional encryption. The master public key and the master secret key involve a risk of deterioration over time just like a public key in general public key cryptography does, and must therefore be updated periodically.
When the master public key and the master secret key are updated, all ciphertexts and all user secret keys must also be updated.
Non-Patent Literature 1 describes update of a master public key and master secret key in ID-based encryption. Non-Patent Literature 1 also describes that when the master public key and the master secret key are updated, a user secret key is not reissued but is updated to cope with this.
Non-Patent Literature 2 describes an encryption scheme that can maintain the security even if information of a master secret key leaks somewhat.